Demonstration of Monogamy Relations for Einstein-Podolsky-Rosen Steering in Gaussian Cluster States

Abstract

A note on versions:The version presented here may differ from the published version or from the version of record. If you wish to cite this item you are advised to consult the publisher's version. Please see the repository url above for details on accessing the published version and note that access may require a subscription. Understanding how quantum resources can be quantified and distributed over many parties has profound applications in quantum communication. As one of the most intriguing features of quantum mechanics, Einstein-Podolsky-Rosen (EPR) steering is a useful resource for secure quantum networks. By reconstructing the covariance matrix of a continuous variable four-mode square Gaussian cluster state subject to asymmetric loss, we quantify the amount of bipartite steering with a variable number of modes per party, and verify recently introduced monogamy relations for Gaussian steerability, which establish quantitative constraints on the security of information shared among different parties. We observe a very rich structure for the steering distribution, and demonstrate one-way EPR steering of the cluster state under Gaussian measurements, as well as one-to-multimode steering. Our experiment paves the way for exploiting EPR steering in Gaussian cluster states as a valuable resource for multiparty quantum information tasks.

Complementary quantum correlations among multipartite systems

“…In [3][4][5], the authors have shown that the xth power of the entanglement of formation (x ≥ √ 2) and the concurrence (x ≥ 2) satisfy multiqubit monogamy inequalities. Monogamy relations for quantum steering have also been demonstrated in [17][18][19][20][21]. Later, polygamy inequalities were proposed in terms of the αth (0 ≤ α ≤ 1) power of square of convex-roof extended negativity (SCREN) and the entanglement of assistance [14,22].…”

Generation of One‐Way Gaussian Steering by Gaussian Channel and Converting One‐Way Gaussian Steering by Beamsplitters

“…Especially, the atomic or solid state-based encoding of continuous variable systems provide a novel method that can be used for quantum information processing. Based on the above two methods, various progress has thoroughly investigated the generation of bipartite or multipartite Gaussian steering, one-way Gaussian steering, [30][31][32] and the potential applications such as one-sided device-independent QKD, [16] and secure quantum teleportation. [20][21][22][23][24][25][26] Gaussian steering is the quantum steering for Gaussian states under Gaussian measurement.…”

Applications of EPR steering in quantum teleportation and NOON states

“…[19,26]. There has also been recent work on quantification of steering [17,27,28], monogamy relations [29,30,31], and multipartite steering [18,32]. Recently it has been shown the existence of steering inequalities for NOON states [2].…”